Self-organization, in one of its accepted definitions, is the appearance of non-random structures in a system without explicit constraints from forces outside the system. In this thesis two self-organizing systems are studied from the viewpoint of mechanics. In the first system—semiconductor crystal surfaces—the internal constraints that lead to self-assembly of nanoscale structures on silicon-germanium (SiGe) films are studied. In the second system—actin cytoskeleton—a consequence of dynamic self-organization of actin filaments in the form of motion of micron-sized beads through a cytoplasmic medium is studied.

When Ge film is deposited on Si(001) substrate, nanoscale features form on the surface and self-organize by minimizing energy contributions from the surface and the strain resulting from difference in lattice constants of the film and the substrate. Clean Si(001) and Ge(001) surfaces are very similar, but experiments to date have shown that atomic scale defects such as dimer-vacancies self-organize into vacancy lines only on Si(001). Through atomic simulations, we show that the observed difference originate from the magnitude of compressive surface strain which reduces formation energy of the dimer-vacancies. During initial stages of the film deposition, the surface is composed of steps and vacancy lines organized in periodic patterns. Using theory of elasticity and atomic simulations we show that these line defects self-organize due to monopolar nature of steps and dipolar nature of the vacancy lines. This self-organized pattern further develops to form pyramidal islands bounded with (105) facets and high Ge content. Mismatch strain of the island is then reduced by incorporation of Si from the substrate surrounding the island leaving behind trenches whose depth is proportional to the basewidth of the island. Using finite element simulations we show that such a relationship is an outcome of competition between elastic energy and surface energy. Some experimental studies also report observation of steeper (103) and (104) facets on pyramidal islands. Using numerical simulations we derive a phase diagram which shows that the steeper facets are stabilized because they provide better relaxation of mismatch strain with only slight increase in surface energy.

In the second system, the actin cytoskeleton is a key structural and propulsion element of eukaryotic cells. Micron-sized "cargoes", which under pathological conditions include bacteria, are propelled by dynamic self-organization of the actin filaments. Recently it is shown that the trajectories of a bacterium, Listeria monocytogenes, propelled by actin filaments are periodic; implying that the organization of actin filaments impart an effective force that spins about the axis of the bacterium. We show that the motion of spherical beads is also non-random; the effective force has an additional degree of freedom due to the spherical symmetry of the bead. Agreement of the theoretical trajectories with experimental observations suggest that the actin-based motility can be generally described using deterministic equations. We also propose microscopic basis for the effective force model which can guide development of microscopic theory to predict the long term trajectories of actin propelled objects.